QC801: Introduction to Quantum Computing
The Study Board for Science
Teaching language: English
EKA: N310085102
Assessment: Second examiner: External
Grading: 7-point grading scale
Offered in: Odense
Offered in: Autumn
Level: Master
STADS ID (UVA): N310085101
ECTS value: 10
Date of Approval: 22-04-2025
Duration: 1 semester
Version: Archive
Entry requirements
Academic preconditions
Students following the course are expected to be acquainted with linear algebra (corresponding to the completion of an introductory course such as MM505 or DM545) and the fundamentals of probability theory.
Course introduction
The overarching goal of quantum computing is to use quantum mechanics for computations and information processing. Utilizing quantum phenomena such as superposition, wave function collapse and entanglement, this leads in many important cases to so-called quantum algorithms, which outperform classical algortihms. Notable examples hereof include factorization of primes, simulation of quantum many-body systems and search algorithms. The central aim of this course is to give students an introduction to quantum computing and some of its central applications, with a particular focus on the Hilbert space formalism that forms the mathematical foundation for all subsequent studies of quantum computing, e.g., in quantum algorithms and protocols, quantum information theory, and much more. While some practical aspects of quantum computing will be covered during the course, the focus of the course is primarily foundational and theoretical.
Expected learning outcome
At the end of the course, students are expected to be able to:
- Describe the postulates of quantum mechanics and their relation to quantum computing;
- Classify separable states and entangled states of joint quantum systems;
- Compute measurement statistics and post-measurement states for measurement operators on small-but-realistic quantum systems;
- Define and explain the role of observables in quantum measurement, and distinguish between measurement by sets of measurement operators, projective measurements, and POVMs;
- Account for central quantum algorithms and protocols, argue for their correctness, and compare them to the best known classical analogues;
- Create and analyse simple quantum circuits.
Content
In addition to an introduction to the pure state formalism of quantum computing (Hilbert spaces, unitaries, measurement, joint systems), this course will cover a selection of the following topics:
- Classical and quantum circuits, circuit complexity, universality, universal gate sets.
- Contextuality and nonlocality, Bell’s theorem, Kochen-Specker theorem, nonlocal games.
- Algorithms (e.g., Deutsch-Jozsa, Grover search, Shor’s algorithm) and protocols (e.g., quantum teleportation, superdense coding) exhibiting quantum advantage.
- Fundamentals of error correction and fault tolerance, stabilizer codes, Gottesman-Knill theorem, threshold theorem.
Literature
Nielsen, M. A. and Chuang, I. L. (2010). Quantum Computation and Quantum Information (10th Anniversary Edition).
Cambridge University Press.
Scherer, W. (2019) Mathematics of Quantum Computing. Springer
Examination regulations
Exam element a)
Timing
Autumn and January
Tests
Portfolio
EKA
N310085102
Assessment
Second examiner: External
Grading
7-point grading scale
Identification
Full name and SDU username
Language
English
Duration
Oral exam - 30 minutes + 30 minutes preparation
Examination aids
All common aids allowed during preparation. Only notes prepared during the preparation time may be brought to the exam itself.
ECTS value
10
Additional information
Portfolio consisting of the following elements:
- A number of assignments handed in during the course
- Final oral exam during the exam period
To achieve a passing grade overall, both elements 1 and 2 must individually meet the learning objectives. The assessment of element 1 takes place in conjunction with the completion of element 2.
The grade is primarily based on element 2, but element 1 can raise or lower the grade by one grade step.
Indicative number of lessons
Teaching Method
Planned lessons:
Total number of planned lessons: 70
Hereof:
Common lessons in classroom/auditorium: 42
Team lessons in classroom: 28
During the common lessons, there will be lectures and group work. During the team lessons, there will be group work and student presentations.
Other planned teaching activities:
Outside the planned lessons, there will be self study, in particular preparation for planned lessons and the exam as well as work on assignments.
Teacher responsible
| Name | Department | |
|---|---|---|
| Matthias Oliver Wilhelm | mwilhelm@imada.sdu.dk | Institut for Matematik og Datalogi |
Additional teachers
| Name | Department | City | |
|---|---|---|---|
| Konstantin Wernli | kwernli@imada.sdu.dk | Institut for Matematik og Datalogi |